Results 61 to 70 of about 122,808 (179)

Quaternion constituents of group algebras [PDF]

Proceedings of the American Mathematical Society, 1971
In this paper it is shown that each quaternion division algebra central over the rationals appears as a division ring constituent of some rational group algebra.
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Orders in quaternion algebras

, 1989
The authors define and study the arithmetic of special orders in quaternion division algebras over number fields. Special orders are analogous to orders of the form \(\left( \begin{matrix} Z\\ NZ\end{matrix} \begin{matrix} Z\\ Z\end{matrix} \right)\) in \(Mat(2,{\mathbb{Q}}_ p)\) and include maximal and Eichler orders as special cases.
Hijikata, H., Pizer, A., Shemanske, T.
openaire   +1 more source

Some properties of octonion and quaternion algebras

, 2006
In 1988, J.R. Faulkner has given a procedure to construct an octonion algebra on a finite dimensional unitary alternative algebra of degree three over a field K. Here we use a similar procedure to get a quaternion algebra.
Bovdi, Victor
core   +1 more source

Generalized Pauli Fibonacci Polynomial Quaternions

Axioms
Since Hamilton proposed quaternions as a system of numbers that does not satisfy the ordinary commutative rule of multiplication, quaternion algebras have played an important role in many mathematical and physical studies.
Bahadır Yılmaz, Nazmiye Gönül Bilgin, Yüksel Soykan   +2 more
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Ideal classes of orders in quaternion algebras [PDF]

We provide an algorithm that, given any order O in a quaternion algebra over a global field, computes representatives of all right equivalence classes of right O-ideals, including the non-invertible ones.
Smit, Harry, Marseglia, Stefano, Voight, John, Fundamental mathematics, Sub Fundamental Mathematics   +4 more
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Quadratic forms and Linkage of Quaternion Algebras

, 1988
A field F satisfies n-linkage on a subset of Ḟ if whenever the quaternion algebrasare equal in Br(F) there exist z ∈ Ḟ withfor i = 1, 2, . . ., n. This linkage of quaternion algebras is examined and its relationship to the torsion freeness of I2(F) and ...
Vatsala Krishnamani, Joseph Yucas
core   +1 more source

Hyperbolic Lattices Derived From Denser Tessellations

IEEE Access
The paper’s aims are threefold. First, to identify the Fuchsian groups associated with the $\{4\lambda, 4\}$ and $\{6\lambda, 3\}$ hyperbolic tessellations in quaternion orders, where $\lambda = 3^{n}$ .
Catia Regina de Oliveira Quilles Queiroz, Vandenberg Lopes Vieira, Giuliano Gadioli la Guardia, Clarice Dias de Albuquerque, Anderson Jose de Oliveira, Leandro Bezerra de Lima, Reginaldo Palazzo   +6 more
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Counting zeros in quaternion algebras using Jacobi forms [PDF]

, 2019
We use the theory of Jacobi forms to study the number of elements in a maximal order of a definite quaternion algebra over the field of rational numbers whose characteristic polynomial equals a given polynomial. A certain weighted average of such numbers
Boylan, H., Skoruppa, N., Zhou, H.
core   +1 more source

Linked triples of quaternion algebras [PDF]

Pacific Journal of Mathematics, 2014
Let \(F\) be a field of characteristic not \(2\). A collection \(Q_1,\ldots,Q_n\) (\(n\geq 2\)) of quaternion algebras over \(F\) is said to have a common slot if there exist \(a,b_i\in F^*\) with \(Q_i\cong (a,b_i)\), \(1\leq i\leq n\). This collection is said to be linked if any pair \(Q_i,Q_j\) has a common slot. \textit{E. Peyre} [Proc. Symp.
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Liftings of reduction maps for quaternion algebras

We construct liftings of reduction maps from complex multiplication (CM) points to supersingular points for general quaternion algebras and use these liftings to establish a precise correspondence between CM points on indefinite quaternion algebras with ...
Jetchev, Dimitar, Cornut, Christophe
core   +1 more source